No Faith In MonkeyGod: A Fine-Tuned Critique of Victor Stenger (Part 2)

[Edit, 4/2/2012: I’ve written a more complete critique of Stenger’s book The Fallacy of Fine-Tuning: Why the Universe Is Not Designed for Us. It’s posted on Arxiv. In particular, the program MonkeyGod is critiqued in Appendix B; most of the points raised below remain valid.]

This post is the second critiquing Victor Stenger’s take on the fine-tuning of the universe for intelligent life. Here are some more of Stenger’s claims. (The quotes below are an amalgam of the articles on this page.)

I think it is safe to conclude that the conditions for the appearance of a universe with life are not so improbable as the those authors, enamored by the anthropic principle, would have you think … [T]here could be many ways to produce a universe old enough to have some form of life.

How does Stenger reach this conclusion?

I have written a program, MonkeyGod … I have studied how the minimum lifetime of a typical star depends on three parameters: the masses of the proton and electron and the strength of the electromagnetic force. (The strong interaction strength does not enter into this calculation.) Varying these parameters by ten orders of magnitude around their present values, I find that over half of the stars will have lifetimes exceeding a billion years, allowing sufficient time for some kind of life to evolve. Long stellar lifetime is not the only requirement for life, but it certainly is not an unusual property of universes.

Warning: long post. Here’s the abstract: Stenger attempts to show that our universe isn’t really fine-tuned by showing that long-lived stars are not unusual. He fails for five reasons. 1.) He gets his formula wrong, and in so doing ignores an important case of fine-tuning. 2.) He fails to consider the effect of altering the strength of gravity. 3.) He “cherry-picks” a very favourable fine-tuning example to suit his purposes. 4.) His probability claims are vacuous, following trivially from his unjustified hidden assumptions. 5.) He rightly exhorts us to consider varying multiple parameters at once, but commits the opposite mistake: he fails to consider multiple life-permitting criteria. Even if he were right about long-lived stars, it doesn’t follow that life-permitting universes do not need to be fine-tuned. I conclude that Stenger’s claims are worse than mistaken; they are misleading.

Let’s have a closer look at Stenger’s claims. He uses the following order-of-magnitude estimate for the lifetime of a main sequence star ():

(1)

where is the fine structure constant, is the dimensionless gravitational strength, () is the proton (electron) mass, (h_bar) and c as usual.

He then varies , and by up to 5 orders of magnitude above and below their value in our universe. After sampling 100 “universes”, he arrives at the following distribution for :

Stenger then notes that about half of the universes have years. He concludes that long-lived stars don’t require much fine-tuning.

I have a number of points to make in response to Stenger’s work.

1. Equation (1) is wrong. Significantly wrong. The correct expression can be found in “Why the universe is just so” by Craig Hogan, along with a brief derivation. The right hand side of (1) needs to be multiplied by , which is the fraction of the total mass-energy () of the star that is released through nuclear reactions. In our universe, .

The inclusion of has a number of effects. Firstly, it reduces the lifetime of a given universe by more than two orders of magnitude. Secondly, depends on the strong force. It should be intuitively obvious that the strong force, which governs nuclear reactions, should be relevant to the lifetime of stars, which are essentially nuclear bombs held together by gravity. Yet Stenger somehow misses this, incorrectly asserting: “the strong interaction strength does not enter into this calculation”. Thus, Stenger fails to account for the effects of altering the strong force.

Most importantly, is a very good example of a fine-tuned constant. When MartinRees chooses “Just Six Numbers” as the best examples of fine-tuned physical parameters, is one of them. In particular, is the parameter that Rees uses to illustrate the fine-tuning needed to produce life-permitting stars. If were 0.006, deuterium would be unstable, meaning that stars would be unable to produce larger elements. Only hydrogen, no chemistry, no planets, no complex structures. If were 0.008, no hydrogen would have survived the big bang. Stars that aren’t fuelled by hydrogen have their lifetimes reduced by a factor of at least 30. Stenger simply leaves this out.

2. Stenger doesn’t consider the effects of altering gravity. When the lifetime of stars is discussed in the context of the fine-tuning of the universe, the strength of gravity usually makes an appearance. If gravity were stronger by a factor of 3000 or more, stellar lifetimes would be significantly reduced. Is this fine-tuned? If we consider the possible range of the strength of gravity to be equal to the range of known force strengths in our universe, then gravity is fine-tuned to a factor of , or approximately 1 in . ( is the strength of the strong force). You may disagree with this line of reasoning, but then it would be up to you to justify a different range of possibilities or a different probability distribution. More on that topic to come.

[Edit (Jul 12, 2010): Victor has replied in the comments saying that the effect of gravity is taken into account in altering the proton mass. And he’s correct: we can write , so if we hold the Planck mass constant (which is reasonable – we simply regard it as setting the scale of the laws of nature), then altering gravity is equivalent to altering the proton mass. I had wrongly assumed that he did what Barrow and Tipler did, and merely altered . The weakness of gravity is then equivalent to the smallness of the proton mass compared to the Planck mass. In terms of the masses, the proton mass is fine tuned to a factor of , which is the square root of what it was before, and thus significantly larger. Still a small number, though, but now there is an important caveat: to speak of the range of the proton mass is to discuss the Higgs mechanism. I’ll wait to see what Prof. Stenger says about that in his new book before responding.]

3. Stenger chooses a life-permitting criterion (“long-lived-stars”) that is one-sided and continuous. By one-sided, I mean that there is no upper bound on – arbitrarily long-lived stars are permitted. (The need for supernovae to distribute heavy elements across the universe is ignored.) By continuous, I mean that is a smoothly varying (power law) function of the fundamental constants. Contrast this with the mass of the neutron (), which is 0.1% more than (proton). The decay of neutrons into protons in the early universe depends on their mass difference. Thus, as decreases (even by 0.1%), the mass difference changes dramatically from positive to negative, meaning that protons decay into neutrons. This leaves none left over for long-lived stars. This is an example of the sudden, discontinuous change that characterises many of the relationships between physical constants and life-permitting criteria.

By considering a one-sided, continuous life-permitting criterion, Stenger has chosen the most favourable case. He has fine-tuned his example in his favour.

4. The probability distribution for depends on the Probability Density Function (PDF) chosen for each of the parameters that are allowed to vary. For a parameter , with value in our universe, Stenger chooses the following PDF:

for

and zero otherwise, where A is a constant of normalisation. This PDF is uniform in , and the range of is 5 orders of magnitude above and below .

A few comments. This PDF is an extremely important assumption on Stenger’s part, yet he doesn’t even draw attention to it, let alone attempt to justify it. Considering a range of values is fine if you’re only interested in exploring what these other universes are like. But Stenger wants to make probability claims (“half the stars …”). Such claims are completely unjustified while ever is unjustified.

More importantly, Stenger has once again fine-tuned his assumptions. Let’s take a closer look at the resultant PDF for . Stenger only considers 100 universes, which is a rather small number for a Monte Carlo investigation. I’ve repeated Stenger’s calculations with my own code, this time using one million universes.

The red vertical line is the value of in our universe (). What can we see from this plot, which is not clear in Stenger’s? The distribution is symmetric around . Of course it is: we are considering PDF’s for the parameters that are symmetric in log-space around their value in our universe, and is related to these parameters as a nice, smooth power-law. The symmetry of the PDF for follows from the symmetry of the PDF’s for the parameters. And since any value for the stellar lifetime larger than is deemed life-permitting (one-sided criterion), Stenger’s claim that about half of these universes support life is trivial. It follows unavoidably from his (unjustified) choice of PDF. Stenger’s claims that “half of the stars will have lifetimes allowing for some kind of life to evolve … [L]ong stellar lifetimes are certainly not an unusual property of universes” are completely vacuous.

5. Stenger takes others to task for failing to consider the consequences of altering several parameters simultaneously. He says: “changes in other parameters may compensate for the change in a selected parameter, allowing more room for a viable, liveable universe than might otherwise be suspected. We and others have concluded that the so-called fine-tuning is not as fine as has been advertised.”

Stenger is right to exhort us to consider the full parameter space. (I’m looking at you, Hugh Ross.) But recognising “other possibilities” for life is not enough to overturn claims of fine-tuning. Expanding parameter space into other dimensions opens up new possibilities for life-permitting universes, but also increases the amount of “dead-space”. A quote from Richard Dawkins springs to mind: “however many ways there may be of being alive, it is certain that there are vastly more ways of being dead, or rather not alive.” Finding other possibilities for life is not the same as showing that life-permitting universes dominate the space of possible universes. Remember: the claim is not that ours is the only universe that could support life, or that we are the only possible form of life. The claim is that if a universe were chosen at random from the range of possible universes, the probability of that universe being able to support intelligent life is very small. This claim is entirely consistent with the existence of other possibilities for life.

Secondly, and most importantly, Stenger makes the opposite mistake. He considers a range of values for the constants, but does not consider a range of life-permitting criteria. Again, he is choosing the most favourable test case: he considers a one-sided, continuous life-permitting criterion and then looks at all the possible ways to fulfil it, giving him the best chance of claiming “look at all these life-permitting universes!”

The list of life-permitting criteria is immense. Stenger, in his MonkeyGod code, ignores the following constraints on his model universes:

The stability of atoms:

The requirement that atoms larger than carbon are stable against nuclear fission places a lower limit: . Non-compliance is punished with the disintegration of all atoms used by living organisms.

Electrons orbiting atoms with have enough kinetic energy to be unstable to electron-positron pair production. This places an upper limit on .

Complex structures

The relative fluctuation of the positions of ions and electrons in solids is governed by . The heaviness of ions ( small) means that they are essentially fixed, allowing the electrons to flow around them and bind the solid. If were of order unity, the electrons that are supposed to bind the solid would be able to dislodge ions from the lattice, melting the solid. As a result, solids would melt and molecules fall apart. The only structures possible would be like those built using only the strong force – roughly spherically symmetric.

The weakness of EM compared to the strong force, and the smallness of , are required to create a clear energy gap between the regime of chemical and nuclear reactions. The reliable properties of the chemicals in your body would be for nought if the energy released in a chemical reaction could transmute elements into each other.

To overcome the second law of thermodynamics, life needs a stable energy source, and stars are the most likely candidate. To power chemical reactions, the energy of photons from the sun needs to be close to typical molecular binding energies – too high, and molecules are simply disintegrated; too low and chemical systems would be unable to harness the sun’s energy. This coincidence holds because .

Suitable stars: we have already noted the simple dependence of lifetime on the constants, including and its effect on element production and big bang nucleosynthesis.

There are other ways to destroy hydrogen in the early universe. We have already noted the effect of the mass difference of neutrons and protons. The weak force also plays an important role – if it is too weak then there is too little hydrogen left over to power stars.

Oberhummer et al. (1999) showed that a change in the strength of the strong force of 0.4% in either direction renders stars incapable of making both carbon and oxygen. They instead make one at the expense of the other. This would have a dramatic effect on the probability of life developing in such a universe.

Stars also need to be stable. There is an optimum mass range – too small and degeneracy pressure prevents nuclear ignition; too large and radiation pressure can break up the star. If , then this “window of stability” closes and no stars are stable.

Large planets: if gravity were a billion times stronger, then planets would need to be the size of a house in order that large-brained organisms are not crushed. This is not large enough to sustain an ecosystem.

Craig Hogan also places constraints on the masses of elementary particles. See his paper “Why the universe is just so” for more details.

This is not an exhaustive list. Remember: one fine-tuned parameter is enough. One failed life-permitting criterion is too many. Even if Stenger were right about the lifetime of stars, it doesn’t follow that all proposed fine-tunings could be as easily dismissed. Stenger cannot make sweeping generalisations about whether the universe is fine-tuned for life by considering only one life-permitting criteria. He is aware of these other cases of fine-tuning – he describes them in his articles. Yet he does not incorporate these into MonkeyGod, under the pretence that this is just a “toy model.” The aim of a toy model is to teach the basics of more complex models, while not worrying about minor details. MonkeyGod does nothing of the sort. It teaches us precisely nothing.

Allow me to state my conclusions with the kind of candour only allowed in the blogosphere: MonkeyGod is bollocks. It is worse than irrelevant – it is misleading. It is a distraction, encouraging us to simply look the other way, to condescending dismiss the evidence for the fine-tuning of the universe for life. It is utter garbage, thinly concealed behind a veil of mathematics.

The worst part is that others are taking Stenger’s work as the definitive debunking of fine-tuning. Here are some quotes from internet articles and forums about MonkeyGod:

Monkey God is a serious research product, defended at length in a technical article. [LB: the article was published in a philosophical journal of a humanist society. Fail again, Richard Carrier.].

Victor Stenger pretty much thoroughly debunked the premise that the formation of stars in the universe is “a house of cards”. To the contrary: as it turns out, you can alter the fundamental constraints of the universe pretty wildly and still come up with a universe capable of supporting stars.

[MonkeyGod gives us] good evidence that the average universe would live long enough to produce life.

MonkeyGod demonstrates that long-lived stars “occur in a wide range of parameters” … there is no reason to assume a priori that any change would result in the impossibility of life.

I’ve previously indicted Hugh Ross for often assuming the appearance of a “true-believer”: desperately searching for and uncritically accepting any “evidence” for fine tuning. Stenger’s feeble, evasive response to the fine-tuning of the universe evokes the opposite stereotype: the condescending “true-unbeliever” who refuses to engage the evidence, who is not searching for truth at all costs, but is instead rummaging for any excuse to explain it away. And it seems that others have followed him into condescension.

I’m being harsh because I expected more from Stenger. He has produced some excellent, original, thoughtful work on the laws of nature in a naturalistic worldview. One can only hope for better things in his forthcoming book.

(I can also endorse the following reply to Stenger from George Ellis.)

Is it possible that Stenger’s formula is meant to give the lifetime of a *typical* main-sequence star? If we include your 0.007 correction then the resulting time is about 4.7 million years, which is (isn’t it?) far shorter than a typical stellar lifespan in our universe.

(I cross-checked with Hogan’s thing, in case I’d screwed up my calculations. His figures aren’t quite the same as mine — it looks like maybe I dropped a factor of pi/2 somewhere — but they’re close enough. Hogan does, in any case, make it clear that his formula is for the *minimum* lifetime of a hydrogen-burning star, and that the range of lifetimes is quite large.)

Remember that epsilon is the fraction of the rest mass energy (Einstein’s E = mc^2) that the star converts into other forms of energy during its lifetime. Thus, if we omit epsilon, we’re not getting a typical main sequence star. It would only be valid for a star that managed to convert its entire rest mass energy into other forms, essentially evapourating itself away. This just doesn’t happen.

Keep in mind that it’s not so much the numerical value that I’m worried about. (I just put the numbers in Google – it does calculations! – and got 0.2 Gyr). In an order of magnitude estimate, being two orders of magnitude off isn’t terrible. The main problem is that epsilson is very plausibly fine tuned – see Martin Rees book “Just Six Numbers”.

I think we may be talking past one another. (Perhaps this is because I’ve screwed up in some way so that what I’m saying doesn’t make sense.)

First: I am not attempting any sort of comprehensive defence of Stenger’s argument; I’m just commenting on your first objection to it. (So any possible fine-tuning of epsilon is irrelevant *to what I’m saying*, even if it demolishes Stenger’s argument as a whole.)

Second: I appreciate that the numerical values aren’t all that important in themselves. I mentioned the one I did just as evidence that if Stenger wanted to describe *typical* main-sequence lifetimes, the formula with the epsilon does that worse than the formula without. (In our universe.)

According to Hogan, his formula (with the epsilon factor) describes the *minimum possible* lifetime of a main-sequence star. (Or did I misunderstand his article?) I just re-did the calculations again using different tools and different sources of information, and I got the same answer: 4.7Myr. That does indeed seem reasonable (I think — I’m no astrophysicist) as a minimum main-sequence lifetime.

So, if Stenger said “this formula gives the minimum lifetime of a main-sequence star” then, no question, he’d be wrong and I’d agree with your point 1. But what he actually says is “minimum lifetime of a typical star”, which is kinda silly (how can it be minimum *and* typical?) but seems quite likely to mean “typical main-sequence lifetime”. (After all, that’s surely much more relevant to the point at issue than the minimum possible lifetime.)

So I’m wondering whether there’s some implicit (and hence shoddy; let me remind you that I’m commenting *only* on you first criticism of Stenger and not defending him generally) thinking along the following lines: we’ve got this formula, with a factor of epsilon in it, for the minimum possible lifetime of a main-sequence star; we’re interested in the typical lifetime of a main-sequence star; it happens that in our universe you get a pretty decent approximation to that just by dropping the factor of epsilon; since for this calculation we’re not interested in the strong force, let’s just suppose it does whatever it needs to so that the ratio (typical lifetime / minimum lifetime / epsilon), which happens to be 1 in our universe, remains 1 in the others; now proceed.

There’s no question that leaving all this stuff implicit would be a poor way to proceed. There’s not much question that assuming that that ratio stays constant is a bit artificial. (But I’m not quite sure; perhaps you can see it as a dimensionless representation of the strength of the strong force, given all the others, in which case holding it constant would be reasonable.) So (to repeatedly repeat myself again) this is not a general defence of Stenger. But I do think that “Stenger just got it wrong” is only justifiable if he really, truly claimed that his formula gave the minimum possible lifetime for a main-sequence star, and I don’t think he did.

Second: I understand, but you can’t make the formula for the “minimum lifetime” into the “typical lifetime” by ignoring epsilon. Epsilon is not a free parameter to be fit by the data from our universe. It can be calculated (in principle) from the strength of the strong force and various other constants. Setting it to 1 can *only* be valid if stars convert their entire rest mass into other forms of energy. But this simply isn’t true.

Regarding the minimum vs typical – in a sense, Stenger and Hogan are both right. The derivation proceeds as follows: estimate the total available energy to be radiated away, estimate the rate at which it is radiated away (the luminosity – energy per unit time). Then the energy divided by the luminosity gives a rough estimate of how long it will take for a star to radiate away the available energy.

The estimate for the luminosity uses an upper limit – called the Eddington luminosity. Stars can’t be brighter than that or they’d blow off their outer layers (photons have momentum!). Since we have used a large luminosity, we get a “minimum” stellar lifetime.

It turns out that this minimum timescale is pretty close to the typical timescale … within an order of magnitude or two. In other words, stars have a luminosity that is pretty close to the Eddington limit. Thus Stenger is not wrong to use this timescale as a typical timescale. He just get’s the formula wrong. (I assume it was just an accident on Stenger’s part – I’ve made plenty of mistakes dumber than that one!)

Finally, let’s do the calculation in google: copy and paste –

0.007*((1/137^2)/(G*(mass of proton)^2/h/c))*(mass of proton/mass of electron)^2*h/(mass of proton * c^2)

You’re using h; the formula (at least according to both Stenger and Hogan) uses hbar. (2pi)^2 is only a constant factor, but it’s not such a small one. 189M/(2pi^2) ~= 5M.

(Remark: surely 0.2Gy couldn’t possibly be the shortest-possible main-sequence lifespan; a main-sequence star with that lifespan would only be about 3 solar masses, and you can get stars a lot bigger and hence shorter-lived than that.)

I wasn’t claiming that there’s any kind of fundamental reason why ignoring epsilon would have to give the typical (as opposed to the minimal) lifetime. I was saying: it seems to turn out, in our universe at least, that epsilon happens to be close to the ratio of minimal to typical lifetime. In lieu of a difficult analysis (does anyone even know how to do it?) of how the ratio between epsilon and (min/typ) varies in hypothetical different universes, Stenger may simply have chosen to suppose that it remains close to 1. I repeat: if that’s what he was doing then he absolutely should have said so; it’s possible that he did, in fact, simply screw up; but it’s not clear that that’s what actually happened.

Leaving aside the question of how Stenger happened to arrive at his version of the formula, I think the issue is the merits of the following two hypotheses:

1. If you take a random sample of hypothetical universes, we should expect (min/typ) to remain roughly what it is.

2. If you take a random sample of hypothetical universes, we should expect epsilon/(min/typ) to remain roughly what it is.

If #1 is better, then to do Stenger’s calculations right (assuming for the sake of argument that there’s any point in doing so) we should restore the factor of epsilon, then add another fudge factor that happens to be ~1/epsilon, and look at how epsilon varies across the possible worlds we’re interested in.

If #2 is better, then we should instead take out the factor of epsilon, as Stenger (by luck or judgement or whatever) did.

If #1 and #2 are both no good, then of course we should do something else again.

Note well: it is simply not true that omitting epsilon could only be appropriate if stars always converted their whole rest mass into other forms of energy. It could also be appropriate if there were some reason to expect the efficiency of stellar hydrogen-burning to be close to that (min/typ) ratio. And, on the other hand, simply using the formula *with* the epsilon is only appropriate if there’s some reason to expect the (min/typ) ratio to be close to 1. And simply using the formula with the epsilon and an extra correction factor is only appropriate if there’s some reason to expect the (min/typ) ratio to be close to its value in our universe.

(Strictly, for “expect X to be close to Y” above means “hold X=Y while allowing other parameters to vary, when doing a thought-experiment about other possible universes”.)

I have no inkling what actually controls the (min/typ) ratio. I would be very happy to be enlightened on that point.

Well played, sir. I told you I made mistakes! (I just rechecked the plot in the original post, and it’s fine.)

I’m 99.9% sure that that’s not what Stenger has done. Once again – epsilon is what it is, and it must remain in the formula. It is defined as the ratio of the energy in the star which is radiated away to the total rest-mass energy of the star. It is not a fitting parameter.

The obvious question that remains is – how do we turn a minimum stellar lifetime into a typical stellar lifetime? I think Barrow and Tipler (pg 333) do it a different way. Instead of the Eddinton luminosity, they estimate the luminosity by estimating the radiation energy contained in a star, and then estimate the amount of time it takes for all that energy to leave the star via a random walk. They arrive at the formula:
t_star = 10^10 yrs * (M/M_min)^2

where M is the mass of the star, and M_min is the minimum stellar mass (i.e. capable of sustaining nuclear fusion). That’s probably closer to a “typical” stellar lifetime, although perhaps we’re closer to the “maximum” end of the spectrum …

I have since used a more realistic lifetime equation, although the one I used was from the published literature. The results are similar.

Gravity is taken into account through the mass of the proton, as i explained.

My Philo article gives all the references used.

I don’t understand the long critique of my probability argument. All I am saying is the obvious. Low probability happens and you have to compare numbers for alternatives.

In any case, there is so much more to my case against fine-tuning that these one or two objections are no consequence to the final conclusion. I have a book coming out next year called “The Fallacy of Fine-Tuning.” If anyone wants to assist me by commenting on the drafts, please email me and I will send you the location of the drafts and the password.

Greetings Vic and welcome to our humble blog. A few points in response:

1. The point with the missing epsilon is not so much that it changes the results – two orders of magnitude isn’t too bad – but that it ignores the role of the strong force, and in so doing leaves out an important case of fine tuning.

2. I didn’t see the point about gravity in the articles I read, but I’ve since found the relevant argument and I think you’re right. I’ll amend the original post.

Part 1: I took your argument to be: “Sperm + egg = William Lane Craig is a low probability event, and yet here he is. So low probability is not sufficient to discount a chance hypothesis”. That’s true, but now the question is: what are the sufficient conditions to discount chance? I’d say that it’s low probability plus an independently specified rejection region (Fisher) or an alternative hypothesis that explains the data better and has a non-vanishing prior (Bayes). I’d say that the fine-tuning of the universe satisfies these, where the alternative hypothesis need not be a designer – a multiverse will do.

[…] stars that can live to be a billion years old. (A very crude proxy for “livability” and probably false.) What he shows is that some of the parameters are correlated, so if I up the gravitational pull, I […]